How can I get my texture to appear correctly on my cylinder?
This is happening because each side face on your cylindrical chip is having the texture applied to it. What you want to do is UV unwrap the whole edge as one strip rather than having a bunch of overlapping faces. To do this you need to mark some seams to tell blender where to separate the mesh. Mark seam the top and bottom circles and then one vertical edge (You can do with by pressing Space and then searching for "Mark Seam"). 

It will look like this:


From here you should select your whole mesh with A and then press U to unwrap.

You final UV map should look like this:


Your chips top and bottom textures should be aligned with the circles and the side texture should go across all of the side faces.